function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

hypothesis = sigmoid(X*theta);
J = 1/m*sum(-y.*log(hypothesis)-(1-y).*log(1-hypothesis)) + 0.5*lambda/m*(theta(2:end)'*theta(2:end));

n = size(X, 2);
grad(1) = 1/m*dot(hypothesis-y, X(:, 1));
for i = 2 : n
    grad(i) = 1/m*dot(hypothesis-y, X(:, i)) + lambda / m * theta(i);
end

% =============================================================

end
